Symbolic Integration Algorithm Selection with Machine Learning: LSTMs vs Tree LSTMs

TL;DR

This paper explores machine learning models, specifically LSTMs and Tree LSTMs, to improve the selection of sub-algorithms in symbolic integration within computer algebra systems, demonstrating that Tree LSTMs outperform standard LSTMs and existing methods.

Contribution

It introduces a novel approach using Tree LSTMs to represent mathematical expressions for sub-algorithm selection, outperforming traditional LSTM models and existing Maple algorithms.

Findings

Tree LSTM significantly outperforms LSTM in sub-algorithm prediction.

Tree LSTM provides better integration outputs than Maple's current approach.

Tree LSTM's informed representation enhances symbolic integration performance.

Abstract

Computer Algebra Systems (e.g. Maple) are used in research, education, and industrial settings. One of their key functionalities is symbolic integration, where there are many sub-algorithms to choose from that can affect the form of the output integral, and the runtime. Choosing the right sub-algorithm for a given problem is challenging: we hypothesise that Machine Learning can guide this sub-algorithm choice. A key consideration of our methodology is how to represent the mathematics to the ML model: we hypothesise that a representation which encodes the tree structure of mathematical expressions would be well suited. We trained both an LSTM and a TreeLSTM model for sub-algorithm prediction and compared them to Maple's existing approach. Our TreeLSTM performs much better than the LSTM, highlighting the benefit of using an informed representation of mathematical expressions. It is able to produce better outputs than Maple's current state-of-the-art meta-algorithm, giving a strong basis for further research.